The Internal Construction Sequence |
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Though it’s often natural and straightforward to describe a geometry problem in terms of constraints, internally, Geometry Expressions uses constructions.
For example, in the drawing below, AB is constrained to be length c, BC is constrained to be length a, AB is constrained to be perpendicular to BC, BD is constrained to be perpendicular to AC, and D is constrained to lie on AC. ![]() Given this input, Geometry Expressions internally creates a construction sequence such as:
Two points are possible at this distance — either to the left or to the right of the line AB. Geometry Expressions takes its cue from where you drew the line segment and placed the point. If the drawing shows C to the right of AB, Geometry Expressions determines that’s what you intended.
The existence of a construction sequence for Geometry Expressions is not equivalent to a problem being mathematically well defined. Unfortunately, Geometry Expressions’ toolbox of constructions cannot cope with a number of mathematically well defined problems. Nevertheless, with a little ingenuity, you can usually find an alternative way to describe the problem, one that the application can construct. Application-added variables, resolving geometrical ambiguities, and what happens when Geometry Expressions cannot find a construction sequence are all discussed in more detail below. |